Question

The sum of digits in the numerator and the denominator of a fraction is 7. If 1 is added to the numerator of the fraction, the value of the fraction becomes 1. Then that fraction is…

Answer 1

Answer :-

Here, it is saying that sum of numerator and denominator is 7. If 1 is added to the numerator, then the value of fraction will be equal to 1.

So, Let numerator be x

Denominator = 7 - x

1 is added to the numerator -

New Numerator = x + 1

According to the question :-

⇒ $\sf \dfrac{x+1}{7-x} = 1$

⇒ $\sf x + 1 = 7 - x$

⇒ $\sf x + x = 7 - 1$

⇒ $\sf 2x = 6$

⇒ $\sf x = \dfrac{6}{2}$

⇒ $\sf x = 3$

• Numerator = 3
• Denominator = 7 - 3 = 4

Hence,

$\boxed{\sf Fraction = \dfrac{3}{4}}$

Verification :-

Numerator + Denominator = 3 + 4 = 7

1 is added to the numerator :-

New numerator = 3 + 1 = 4

Fraction = 4 / 4 = 1

Hence, verified